Hi,
The simplest thing to do is to try all the options. Build a layer graph for each possible graph that fulfils the requirement of the question. The graphs will have 6 levels, with all the edges on all the levels, and between the levels exactly one edge - a red edge.
So one graph will have the red edges 1,4,5,2,7.
Another would have 4,5,2,1,7 etc. There are a lot of options!!! 10x9x8x7x6 to be precise, but it's a constant number.